{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Deep Q Networks.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "accelerator": "GPU"
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MqLCpeuB1rsn",
        "colab_type": "text"
      },
      "source": [
        "# Q Learning and Deep Q Network Examples"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DNCXqYSN1jeA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import random\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "from collections import deque\n",
        "from time import time"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pZgaI7aE17NT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "3f549114-264d-4add-d57c-fb8f76e2f759"
      },
      "source": [
        "seed = 23041974\n",
        "\n",
        "random.seed(seed)\n",
        "print('Seed: {}'.format(seed))"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Seed: 23041974\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0ioqscIW2DeB",
        "colab_type": "text"
      },
      "source": [
        "### Game design"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "skRGPAnQ2IKi",
        "colab_type": "text"
      },
      "source": [
        "The game the Q-agents will need to learn is made of a board with 4 cells. The agent will receive a reward of +1 every time it fills a vacant cell, and will receive a penalty of -1 when it tries to fill an already occupied cell. The game ends when the board is full."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V8zhwjDu2CG6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class Game:\n",
        "  board = None\n",
        "  board_size = 0\n",
        "  \n",
        "  def __init__(self, board_size = 4):\n",
        "    self.board_size = board_size\n",
        "    self.reset()\n",
        "    \n",
        "  def reset(self):\n",
        "    self.board = np.zeros(self.board_size)\n",
        "    \n",
        "  def play(self, cell):\n",
        "    # Returns a tuple: (reward, game_over?)\n",
        "    if self.board[cell] == 0:\n",
        "      self.board[cell] = 1\n",
        "      game_over = len(np.where(self.board == 0)[0]) == 0\n",
        "      return (1, game_over)\n",
        "    else:\n",
        "      return (-1, False)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aSEtD_D63qSI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 321
        },
        "outputId": "544a5671-5e01-4c41-ec27-3f76ea52db8d"
      },
      "source": [
        "def state_to_str(state):\n",
        "  return str(list(map(int, state.tolist())))\n",
        "\n",
        "all_states = list()\n",
        "for i in range(2):\n",
        "  for j in range(2):\n",
        "    for k in range(2):\n",
        "      for l in range(2):\n",
        "        s = np.array([i, j, k, l])\n",
        "        all_states.append(state_to_str(s))\n",
        "        \n",
        "print('All possible states: ')\n",
        "\n",
        "for s in all_states:\n",
        "  print(s)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "All possible states: \n",
            "[0, 0, 0, 0]\n",
            "[0, 0, 0, 1]\n",
            "[0, 0, 1, 0]\n",
            "[0, 0, 1, 1]\n",
            "[0, 1, 0, 0]\n",
            "[0, 1, 0, 1]\n",
            "[0, 1, 1, 0]\n",
            "[0, 1, 1, 1]\n",
            "[1, 0, 0, 0]\n",
            "[1, 0, 0, 1]\n",
            "[1, 0, 1, 0]\n",
            "[1, 0, 1, 1]\n",
            "[1, 1, 0, 0]\n",
            "[1, 1, 0, 1]\n",
            "[1, 1, 1, 0]\n",
            "[1, 1, 1, 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UYmEVU-C4CDl",
        "colab_type": "text"
      },
      "source": [
        "Initialize the game:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4GYiM4ZE3_yO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "game = Game()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2gAEN83m4Gx6",
        "colab_type": "text"
      },
      "source": [
        "## Q Learning"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Kniwoe2u4JP6",
        "colab_type": "text"
      },
      "source": [
        "Starting with a table-based Q-learning algorithm"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9FN-QW9v4Fgi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "num_of_games = 2000\n",
        "epsilon = 0.1\n",
        "gamma = 1"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tVjczKrb4Q01",
        "colab_type": "text"
      },
      "source": [
        "Initializing the Q-table:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WaJcA3QN4QCr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "q_table = pd.DataFrame(0, \n",
        "                       index = np.arange(4),\n",
        "                       columns = all_states)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NOnU7dG84lcH",
        "colab_type": "text"
      },
      "source": [
        "Letting the agent play and learn:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yXvl_sDH4j9K",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 247
        },
        "outputId": "b96a489e-8177-492b-fee8-e1816c102773"
      },
      "source": [
        "r_list = []    ## Store the total reward of each game so we could plot it later\n",
        "\n",
        "for g in range(num_of_games):\n",
        "  game_over = False\n",
        "  game.reset()\n",
        "  total_reward = 0\n",
        "  while not game_over:\n",
        "    state = np.copy(game.board)\n",
        "    if random.random() < epsilon:\n",
        "      action = random.randint(0, 3)\n",
        "    else:\n",
        "      action = q_table[state_to_str(state)].idxmax()\n",
        "    reward, game_over = game.play(action)\n",
        "    total_reward += reward\n",
        "    if np.sum(game.board) == 4:    ## Terminal state\n",
        "      next_state_max_q_value = 0\n",
        "    else:\n",
        "      next_state = np.copy(game.board)\n",
        "      next_state_max_q_value = q_table[state_to_str(next_state)].max()\n",
        "    q_table.loc[action, state_to_str(state)] = reward + gamma * next_state_max_q_value\n",
        "  r_list.append(total_reward)\n",
        "q_table"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>[0, 0, 0, 0]</th>\n",
              "      <th>[0, 0, 0, 1]</th>\n",
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              "      <th>[0, 1, 0, 0]</th>\n",
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              "      <th>[0, 1, 1, 0]</th>\n",
              "      <th>[0, 1, 1, 1]</th>\n",
              "      <th>[1, 0, 0, 0]</th>\n",
              "      <th>[1, 0, 0, 1]</th>\n",
              "      <th>[1, 0, 1, 0]</th>\n",
              "      <th>[1, 0, 1, 1]</th>\n",
              "      <th>[1, 1, 0, 0]</th>\n",
              "      <th>[1, 1, 0, 1]</th>\n",
              "      <th>[1, 1, 1, 0]</th>\n",
              "      <th>[1, 1, 1, 1]</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>4</td>\n",
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              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>-1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
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              "      <th>2</th>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
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              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>2</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   [0, 0, 0, 0]  [0, 0, 0, 1]  ...  [1, 1, 1, 0]  [1, 1, 1, 1]\n",
              "0             4             3  ...             0             0\n",
              "1             4             0  ...             0             0\n",
              "2             4             0  ...             0             0\n",
              "3             4             0  ...             1             0\n",
              "\n",
              "[4 rows x 16 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VvPp2xEG52gM",
        "colab_type": "text"
      },
      "source": [
        "Let's verify that the agent indeed learned a correct strategy by seeing what action it will choose in each one of the possible states:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kEUwiq1T5yaJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        },
        "outputId": "48e0bca0-e0f3-4c8d-8eda-79ca8901d7b2"
      },
      "source": [
        "for i in range(2):\n",
        "  for j in range(2):\n",
        "    for k in range(2):\n",
        "      for l in range(2):\n",
        "        b = np.array([i, j, k, l])\n",
        "        if len(np.where(b == 0)[0]) != 0:\n",
        "          action = q_table[state_to_str(b)].idxmax()\n",
        "          pred = q_table[state_to_str(b)].tolist()\n",
        "          print('board: {b}\\tpredicted Q values: {p} \\tbest action: {a}\\t correct action? {s}'\n",
        "                .format(b = b, p = pred, a = action, s = b[action] == 0))"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "board: [0 0 0 0]\tpredicted Q values: [4, 4, 4, 4] \tbest action: 0\t correct action? True\n",
            "board: [0 0 0 1]\tpredicted Q values: [3, 0, 0, 0] \tbest action: 0\t correct action? True\n",
            "board: [0 0 1 0]\tpredicted Q values: [3, 1, 2, 1] \tbest action: 0\t correct action? True\n",
            "board: [0 0 1 1]\tpredicted Q values: [2, 0, 0, 0] \tbest action: 0\t correct action? True\n",
            "board: [0 1 0 0]\tpredicted Q values: [3, 2, 3, 3] \tbest action: 0\t correct action? True\n",
            "board: [0 1 0 1]\tpredicted Q values: [2, 0, 0, 0] \tbest action: 0\t correct action? True\n",
            "board: [0 1 1 0]\tpredicted Q values: [2, 0, 0, 0] \tbest action: 0\t correct action? True\n",
            "board: [0 1 1 1]\tpredicted Q values: [0, 0, 0, 0] \tbest action: 0\t correct action? True\n",
            "board: [1 0 0 0]\tpredicted Q values: [2, 3, 3, 3] \tbest action: 1\t correct action? True\n",
            "board: [1 0 0 1]\tpredicted Q values: [1, 2, 2, 1] \tbest action: 1\t correct action? True\n",
            "board: [1 0 1 0]\tpredicted Q values: [1, 2, 1, 1] \tbest action: 1\t correct action? True\n",
            "board: [1 0 1 1]\tpredicted Q values: [-1, 1, -1, 0] \tbest action: 1\t correct action? True\n",
            "board: [1 1 0 0]\tpredicted Q values: [1, 1, 2, 2] \tbest action: 2\t correct action? True\n",
            "board: [1 1 0 1]\tpredicted Q values: [0, 0, 1, 0] \tbest action: 2\t correct action? True\n",
            "board: [1 1 1 0]\tpredicted Q values: [0, 0, 0, 1] \tbest action: 3\t correct action? True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d-wNz71h6z3y",
        "colab_type": "text"
      },
      "source": [
        "We can see that the agent indeed picked up the right way to play the game. Still, when looking at the predicted Q values, we see that there are some states where it didn't pick up the correct Q values."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xb0DIqqL7H0I",
        "colab_type": "text"
      },
      "source": [
        "Q Learning is a greedy algorithm, and it prefers choosing the best action at each state rather than exploring. We can solve this issue by increasing <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>&#x3B5;</mi></math> (epsilon), which controls the exploration of this algorithm and was set to 0.1, OR by letting the agent play more games."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Sgb7urf87nvD",
        "colab_type": "text"
      },
      "source": [
        "Let's plot the total reward the agent received per game:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ozl5o3SQ6mVQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "outputId": "ffcc8778-af00-4d32-ff49-88bc5dc4a3dc"
      },
      "source": [
        "plt.figure(figsize = (14, 7))\n",
        "plt.plot(range(len(r_list)), r_list)\n",
        "plt.xlabel('Games played')\n",
        "plt.ylabel('Reward')\n",
        "plt.show()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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fcCXD9tkue6t7+XJNqTscqOxh6qzsvg0V0vOYlG1tLFq3qKc6N+SqMJ97JS2V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\nHSEzMzMzM+s67giZmZmZmVnX+R9M3ZNmsEMTgwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 1008x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Cq99Dtkf74rD",
        "colab_type": "text"
      },
      "source": [
        "## Deep Q Network"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nBb2BuWZ8iQu",
        "colab_type": "text"
      },
      "source": [
        "Let's move on to neural network-based modeling. We'll design the Q network first."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h6f2CO378sBu",
        "colab_type": "text"
      },
      "source": [
        "Remember that the output of the network, ```(self.output) ``` is an array of the predicted Q value for each action taken from the input state ``` (self.states)```. Comparing with the Q-table algorithm, the output is an entire column of the table\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vVO9DY7A7y79",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class QNetwork:\n",
        "  \n",
        "  def __init__(self, hidden_layers_size, gamma, learning_rate,\n",
        "               input_size = 4, output_size = 4):\n",
        "    self.q_target = tf.placeholder(shape = (None, output_size), dtype = tf.float32)\n",
        "    self.r = tf.placeholder(shape = None, dtype = tf.float32)\n",
        "    self.states = tf.placeholder(shape = (None, input_size), dtype = tf.float32)\n",
        "    self.enum_actions = tf.placeholder(shape = (None, 2), dtype = tf.int32)\n",
        "    layer = self.states\n",
        "    for l in hidden_layers_size:\n",
        "      layer = tf.layers.dense(inputs = layer, units = l, \n",
        "                              activation = tf.nn.relu,\n",
        "                              kernel_initializer = tf.contrib.layers.xavier_initializer(seed = seed))\n",
        "    self.output = tf.layers.dense(inputs = layer, units = output_size,\n",
        "                                  kernel_initializer = tf.contrib.layers.xavier_initializer(seed = seed))\n",
        "    self.predictions = tf.gather_nd(self.output, indices = self.enum_actions)\n",
        "    self.labels = self.r + gamma * tf.reduce_max(self.q_target, axis = 1)\n",
        "    self.cost = tf.reduce_mean(tf.losses.mean_squared_error(labels = self.labels,\n",
        "                                                            predictions = self.predictions))\n",
        "    self.optimizer = tf.train.GradientDescentOptimizer(learning_rate = learning_rate).minimize(self.cost)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gfUsSy8k1DA8",
        "colab_type": "text"
      },
      "source": [
        "Designing the **Experience Replay memory** which will be used, using a cyclic memory buffer:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zBMdWdxt1BNk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class ReplayMemory:\n",
        "  memory = None\n",
        "  counter = 0\n",
        "  \n",
        "  def __init__(self, size):\n",
        "    self.memory = deque(maxlen = size)\n",
        "    \n",
        "  def append(self, element):\n",
        "    self.memory.append(element)\n",
        "    self.counter += 1\n",
        "    \n",
        "  def sample(self, n):\n",
        "    return random.sample(self.memory, n)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1t9m6EFk2HyD",
        "colab_type": "text"
      },
      "source": [
        "Setting up the parameters. Note that here we used `gamma = 0.99` and not 1 like in the Q-table algorithm, as the literature recommends working with a discount factor of **<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>0</mn><mo>.</mo><mn>9</mn><mo>&#xA0;</mo><mo>&#x2264;</mo><mo>&#xA0;</mo><mi>&#x3B3;</mi><mo>&#xA0;</mo><mo>&#x2264;</mo><mo>&#xA0;</mo><mn>0</mn><mo>.</mo><mn>99</mn></math>**. It probably won't matter much in this specific case, but it's good to get used to this.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ypu5eaS92GRT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "num_of_games = 2000\n",
        "epsilon = 0.1\n",
        "gamma = 0.99\n",
        "batch_size = 10\n",
        "memory_size = 2000"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SCC_xpF524iX",
        "colab_type": "text"
      },
      "source": [
        "Initializing the Q-network:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fZAuXwb923uf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 91
        },
        "outputId": "1c572031-b983-4dbe-d6af-6ebc1025c097"
      },
      "source": [
        "tf.reset_default_graph()\n",
        "tf.set_random_seed(seed)\n",
        "qnn = QNetwork(hidden_layers_size = [20, 20],\n",
        "               gamma = gamma,\n",
        "               learning_rate = 0.001)\n",
        "memory = ReplayMemory(memory_size)\n",
        "sess = tf.Session()\n",
        "sess.run(tf.global_variables_initializer())"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/losses/losses_impl.py:121: add_dispatch_support.<locals>.wrapper (from tensorflow.python.ops.array_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.where in 2.0, which has the same broadcast rule as np.where\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hfhSAmOc3Z8m",
        "colab_type": "text"
      },
      "source": [
        "Training the network. Compare this code to the above Q-table training."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cay06IcS3OZF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "14864b0d-cb6b-478e-dceb-d005f48e1990"
      },
      "source": [
        "r_list = []\n",
        "c_list = []    ## Same as r_list, but for storing the cost\n",
        "\n",
        "counter = 0    ## Will be used to trigger network training\n",
        "\n",
        "for g in range(num_of_games):\n",
        "  game_over = False\n",
        "  game.reset()\n",
        "  total_reward = 0\n",
        "  while not game_over:\n",
        "    counter += 1\n",
        "    state = np.copy(game.board)\n",
        "    if random.random() < epsilon:\n",
        "      action = random.randint(0, 3)\n",
        "    else:\n",
        "      pred = np.squeeze(sess.run(qnn.output,\n",
        "                                 feed_dict = {qnn.states: np.expand_dims(game.board, axis = 0)}))\n",
        "      action = np.argmax(pred)\n",
        "    reward, game_over = game.play(action)\n",
        "    total_reward += reward\n",
        "    next_state = np.copy(game.board)\n",
        "    memory.append({'state': state, 'action': action,\n",
        "                   'reward': reward, 'next_state': next_state,\n",
        "                   'game_over': game_over})\n",
        "    if counter % batch_size == 0:\n",
        "      ## Network training\n",
        "      batch = memory.sample(batch_size)\n",
        "      q_target = sess.run(qnn.output, feed_dict = {qnn.states: np.array(list(map(lambda x: x['next_state'], batch)))})\n",
        "      terminals = np.array(list(map(lambda x: x['game_over'], batch)))\n",
        "      for i in range(terminals.size):\n",
        "        if terminals[i]:\n",
        "          ## Remember we use the network's own predictions for the next state while calculating loss.\n",
        "          ## Terminal states have no Q-value, and so we manually set them to 0, as the network's predictions\n",
        "          ## for these states is meaningless\n",
        "          q_target[i] = np.zeros(game.board_size)\n",
        "      _, cost = sess.run([qnn.optimizer, qnn.cost],\n",
        "                         feed_dict = {qnn.states: np.array(list(map(lambda x: x['state'], batch))),\n",
        "                                      qnn.r: np.array(list(map(lambda x: x['reward'], batch))),\n",
        "                                      qnn.enum_actions: np.array(list(enumerate(map(lambda x: x['action'], batch)))),\n",
        "                                      qnn.q_target: q_target})\n",
        "      c_list.append(cost)\n",
        "  r_list.append(total_reward)\n",
        "print('Final cost: {}'.format(c_list[-1]))"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Final cost: 1.1149362325668335\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oYV9qA0R5wwx",
        "colab_type": "text"
      },
      "source": [
        "Again, let's verify that the agent indeed learned a correct strategy:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IDZFlFca5k4o",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 305
        },
        "outputId": "71092db7-ded6-40d7-967e-6d07f818cb58"
      },
      "source": [
        "for i in range(2):\n",
        "  for j in range(2):\n",
        "    for k in range(2):\n",
        "      for l in range(2):\n",
        "        b = np.array([i, j, k, l])\n",
        "        if len(np.where(b == 0)[0]) != 0:\n",
        "          pred = np.squeeze(sess.run(qnn.output, \n",
        "                                     feed_dict = {qnn.states: np.expand_dims(b, axis = 0)}))\n",
        "          pred = list(map(lambda x: round(x, 3), pred))\n",
        "          action = np.argmax(pred)\n",
        "          print('board: {b} \\tpredicted Q values: {p} \\tbest action: {a} \\tcorrect action? {s}'\n",
        "                .format(b = b, p = pred, a = action, s = b[action] == 0))"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "board: [0 0 0 0] \tpredicted Q values: [-0.501, -0.503, -0.567, -0.495] \tbest action: 3 \tcorrect action? True\n",
            "board: [0 0 0 1] \tpredicted Q values: [-0.318, 0.244, 0.207, -1.017] \tbest action: 1 \tcorrect action? True\n",
            "board: [0 0 1 0] \tpredicted Q values: [-0.147, -0.003, -0.858, -0.681] \tbest action: 1 \tcorrect action? True\n",
            "board: [0 0 1 1] \tpredicted Q values: [0.257, 0.535, -0.509, -1.026] \tbest action: 1 \tcorrect action? True\n",
            "board: [0 1 0 0] \tpredicted Q values: [-0.422, -1.015, -0.444, -0.342] \tbest action: 3 \tcorrect action? True\n",
            "board: [0 1 0 1] \tpredicted Q values: [-0.006, -0.148, 0.154, -0.774] \tbest action: 2 \tcorrect action? True\n",
            "board: [0 1 1 0] \tpredicted Q values: [0.216, -0.856, -0.716, -0.165] \tbest action: 0 \tcorrect action? True\n",
            "board: [0 1 1 1] \tpredicted Q values: [0.721, -0.119, -0.333, -0.626] \tbest action: 0 \tcorrect action? True\n",
            "board: [1 0 0 0] \tpredicted Q values: [-1.481, -0.814, -0.931, -1.023] \tbest action: 1 \tcorrect action? True\n",
            "board: [1 0 0 1] \tpredicted Q values: [-0.763, -0.101, -0.307, -1.308] \tbest action: 1 \tcorrect action? True\n",
            "board: [1 0 1 0] \tpredicted Q values: [-0.976, -0.362, -1.192, -1.013] \tbest action: 1 \tcorrect action? True\n",
            "board: [1 0 1 1] \tpredicted Q values: [-0.318, 0.485, -0.675, -1.482] \tbest action: 1 \tcorrect action? True\n",
            "board: [1 1 0 0] \tpredicted Q values: [-1.265, -1.549, -0.81, -0.607] \tbest action: 3 \tcorrect action? True\n",
            "board: [1 1 0 1] \tpredicted Q values: [-0.628, -0.784, -0.113, -1.084] \tbest action: 2 \tcorrect action? True\n",
            "board: [1 1 1 0] \tpredicted Q values: [-0.703, -1.186, -1.043, -0.539] \tbest action: 3 \tcorrect action? True\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5MlhC9A_6vAr",
        "colab_type": "text"
      },
      "source": [
        "Here too, we see that the agent learned a correct strategy, and again, Q values are not what we would've expectdd."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4mhd5oY9658M",
        "colab_type": "text"
      },
      "source": [
        "Let's plot the rewards the agent received:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qd90SDmv6pWX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "outputId": "f755dab0-1386-46db-df7d-33b309f89de6"
      },
      "source": [
        "plt.figure(figsize = (14, 7))\n",
        "plt.plot(range(len(r_list)), r_list)\n",
        "plt.xlabel('Games played')\n",
        "plt.ylabel('Reward')\n",
        "plt.show()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PURJhKvs1qQS+fclC9LbaE0FlYwNqHh7D0ebG+zcIDYhzvvMA/u224m1fvfUA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\n",
            "text/plain": [
              "<Figure size 1008x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eTHLJpNz7ILd",
        "colab_type": "text"
      },
      "source": [
        "Zooming in, so we can compare the Q-table algorithm:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7eFgrVv-7EYV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "outputId": "9c77e229-4097-4864-b28b-b33067a3da73"
      },
      "source": [
        "plt.figure(figsize = (14, 7))\n",
        "plt.plot(range(len(r_list)), r_list)\n",
        "plt.xlabel('Game played')\n",
        "plt.ylabel('Reward')\n",
        "plt.ylim(-2, 4.5)\n",
        "plt.show()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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cWRR7otoDVRHIX9DRl0GYH1uXwq5apF8nivOjFImYLo0zdaoQppXcZKvKRNxN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\nARk/r9ARCaCPAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1008x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bnHs_fyF7X__",
        "colab_type": "text"
      },
      "source": [
        "Let's plot the cost too. Remember that here the x-axis reflects the number of trainings, and not the number of games. The number of training depends on the number of actions taken, and the agent can take any number of actions during each game."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U8Rc2ksK7UMR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "outputId": "0c2304aa-951b-4e13-c5ec-d07db7e1d8a8"
      },
      "source": [
        "plt.figure(figsize = (14, 7))\n",
        "plt.plot(range(len(c_list)), c_list)\n",
        "plt.xlabel('Trainings')\n",
        "plt.ylabel('Cost')\n",
        "plt.show()"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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wE1TdGOmyc5z+BfmSpMaWWPoHBHIEAQgAgJDI5elhSE3/Pm0BiBEgwC4CEAAA6NHG4tQW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\nGE6AzMzMzMysMJwAmZmZmZlZYfw/h3qA/FoTHdEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1008x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}
